Related papers: Affine Almost Automorphic Actions on Compact Nilma…
Ray nil-affine geometries are defined on nilpotent spaces. They occur in every parabolic geometry and in those cases, the nilpotent space is an open dense subset of the corresponding flag manifold. We are interested in closed manifolds…
We study orbit closures and stationary measures for groups of automorphisms of $p$-adic affine surfaces.
Affine manifolds are called integral if there is an atlas such that all transition maps are affine transformations with integer matrices of linear parts. In this paper we describe all complete integral affine structures on compact…
In this article we introduce a class of discontinuous almost automorphic functions which appears naturally in the study of almost automorphic solutions of differential equations with piecewise constant argument. Their fundamental properties…
Every partially hyperbolic diffeomorphism on a 3-dimensional nilmanifold is leaf conjugate to a nilmanifold automorphism.
We show that every reductive subgroup of the automorphism group of a quasi-smooth well formed weighted complete intersection is a restriction of a subgroup in the automorphism group in the ambient weighted projective space. Also, we provide…
We approximate smooth maps defined on non-compact totally real manifolds by holomorphic automorphisms of $\mathbb C^n$.
We study the automorphism group of graphons (graph limits). We prove that after an appropriate "standardization" of the graphon, the automorphism group is compact. Furthermore, we characterize the orbits of the automorphism group on…
We study dynamical properties of automorphisms of compact nilmanifolds and prove that every ergodic automorphism is exponentially mixing and exponentially mixing of higher orders. This allows to establish probabilistic limit theorems and…
We study automorphisms of the affine line over rings like ZZ/p^n.
If $f$ is an automorphism of a compact simply connected K\"ahler manifold with trivial canonical bundle that fixes a K\"ahler class, then the order of $f$ is finite. We apply this well known result to construct compact non-K\"ahler…
In this paper, we study the isotropy subgroups of some almost rigid domains and give necessary and sufficient conditions for an automorphism to be in the isotropy subgroup.
We prove the rigidity and vanishing of several indices of "geometrically natural" twisted Dirac operators on almost even-Clifford Hermitian manifolds admitting circle actions by automorphisms.
We show that a complex normal surface singularity admitting a contracting automorphism is necessarily quasihomogeneous. We also describe the geometry of a compact complex surface arising as the orbit space of such a contracting…
In this paper we study domains in flag manifolds which are bounded in an affine chart and whose projective automorphism group acts co-compactly. In contrast to the many examples in real projective space, we will show that no examples exist…
We investigate the action of the automorphism group of a closed Riemann surface on its set of theta characteristics (or spin structures). We give criteria for when an automorphism fixes all spin structures, or when it fixes just one. The…
We construct examples of two-step and three-step nilpotent Lie groups whose automorphism groups are `small' in the sense of either not having a dense orbit for the action on the Lie group, or being nilpotent (the latter being stronger).…
We study the automorphisms group action on a bounded domain in $\CC^n$ having a boundary point that is exponentially flat. Such a domain typically has a compact automorphism group. Our results enable us to generate many new examples.
This is an expository article on properties of actions on Lie groups by subgroups of their automorphism groups. After recalling various results on the structure of the automorphism groups, we discuss actions with dense orbits, invariant and…
Extending well-known results on surfaces, we give bounds on the cohomological action of automorphisms of compact K\"ahler threefolds. More precisely, if the action is virtually unipotent we prove that the norm of $(f^n)^*$ grows at most as…